The Model Reduction Of Complex Beam Type Structure And Modification Of Model Reduction

In the modern engineering calculations, we usually have to handle dynamics analysis and optimization of complex slender structure such as aircraft. Using the finite element technique, we can easily construct the fine FEM model for static analysis of such complicated structures. However, due to time-consuming computations of dynamic analysis and optimization, it is almost impossible to optimize structural dynamic performances based on the fine FEM model. Therefore, based on the fine FEM model of such complicated structures, constructing an approximate a reduced model which can meet of the engineering calculations, which is still very valuable in many design departments.Based on the plane section assumption of the beam theory, displacement of FEM nodes in each cross section is approximated by the motion of centroid of the cross section through the displacement transformation matrix. The model reduction method is further improved by including displacement interpolation function of beam and constructing a new physical reduced base vectors. This improvement solves the deficiency of the restrictions on regular finite element grid and large size of the reduced model, and makes the method applicable for more complicated FEM models of arbitrary meshes and geometry. Based on the presented model reduction method, slender structure is divided into several beam part and each part is reduced to a super beam element, resulting in a free-free reduced super beam model. Frequency analysis of the free-free reduced super beam model in a variety of boundary conditions is carried out. The frequency analysis results shows that the reduced super beam not only has high computational accuracy and efficiency, and can handle different situations for a wide range. But some of the modal parameters in the super beam model will bring errors. Therefore, the super beam model requires revision.This article adopts auto-oscillation model test to carry out the model analysis of a cylindrical shell structure which is lifted with a rubber rope to simulate the free state of freedom, which identify the preliminary modes, including natural frequencies and mode shapes. This article uses ANSYS to establish the fine FEM model of cylindrical shell structure. The model reduction method based on the plane section assumption of the beam theory and displacement interpolation function of beam to establish a super beam model. Meanwhile, the super beam model of degrees of freedom correspond with the measured degree of freedom. This article introduces the concept of shear correction factor of super beam model, shear correction factor as optimization parameters to modify the super beam model. Taking the preliminary overall frequencies and mode result as restrains, the article uses the SCE-UA multipolar domain under the global optimal solution of the algorithm to modify the super beam model and the natural frequencies and vibration modes of modified the super beam model matches the data from experiment better.